Hilbert matrix
Syntax
H = hilb(n)
Description
H = hilb(n)
returns the Hilbert matrix of order n.
Definition
The Hilbert matrix is a notable example of a poorly conditioned matrix [1]. The elements of the Hilbert matrices are
.
Examples
Even the fourth-order Hilbert matrix shows signs of poor conditioning.
cond(hilb(4)) =
1.5514e+04
Algorithm
See the M-file for a good example of efficient MATLAB programming where conventional for loops are replaced by vectorized statements.
See Also
invhilb Inverse of the Hilbert matrix
References
[1] Forsythe, G. E. and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, 1967, Chapter 19.
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